Continuity of the SLE trace in simply connected domains

We prove that the SLE _κ trace in any simply connected domain G is continuous (except possibly near its endpoints) if κ < 8. We also prove an SLE analog of Makarov’s Theorem about the support of harmonic measure.     

Quantenstatistische Zustandsgleichung von stark ionisierten Wasserstoffplasmen mittlerer Dichte

A quantum statistical formula for the equation of state of fully ionized plasmas in the mean temperature and mean density region is given. The complete second virial coefficient for the case of Debye screening is taken into account. The binary Slater sums are represented by interpolation between the analytical expressions for small and for large radii respectively. Using the interpolation formulae the equation of state is calculated numerically for the temperatures T = 20000 K and T = 80000 K. The resulting curves are in good agreement with the analytical equation of state for very small densities.     

On the optimum design of piston rings

We study a family of control problems that arise in the design of dynamically loaded bearings which have a minimum power loss; in particular, we study the design of piston rings with minimum parasitic power loss.This research was partially supported by NSF Grant No. MCS-77-05624.     

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Ohne Zusammenfassung     

Variation of the conformal radius

We study the change of the conformal radiusr(U) of a simply connected planar domainU versus the subdomainU _ε consisting of the points of distance at least ε to ∂U. We show that the smallest exponent λ such thatr(U)-r(U _t)=0(e ^λ) satisfies 0.59<λ<0.91. We also show that a well-known conjecture implies . Partially supported by NSF Grant DMS-9970398.